Isoquant or Iso-product curve

Production Function with two Variable Inputs

The prime concern of a firm is to use the cheapest factor combination to produce a given quantity of output. There are a large number of alternative combinations of inputs that can produce a given quantity of output for a given amount of investment­­. Hence, a producer has to select the most economical combination out of them. The most common and simple tool of analysis is the isoquant curve technique which is a parallel concept to the indifference curve in the theory of consumption.

The word “isoquant” simply means equal quantities. Therefore, it is also known as ‘equal product curve’ or ‘production indifference curve’.

It is also called the iso-product curve.

An isoquant curve is a locus of points representing various combinations of two inputs-capital and labor- yielding the same output. In other words, an isoquant curve shows all those combinations of two variable inputs that yield a given quantity of product.

If there are different isoquant curves, they represent different levels of output.

Combinations	Factor X (Labor)	Factor Y (Capital)	Total Output in Units
A	1	12	100
B	2	8	100
C	3	5	100
D	4	3	100
E	5	2	100

Combination-A, representing 1 unit of Factor-X and 12 units of Factor-Y, produces a given quantity (100 units) of a product. All other Combinations B, C, D, E in the table are assumed to yield the same output of the product. If we plot all these combinations on a graph and join them, we shall get a curve called ‘Iso-product Curve’.

IQ represents all those combinations of two factors that produce the same units of the product. The shape of the isoquants shows the degree of substitutability between the two factors used in productions.

Indifference Curve and Isoquant curves distinguished

Though isoquant curves are similar to the indifference curve, one important difference is that the indifference curve shows all those combinations of two goods which provide equal satisfaction to a consumer, it doesn’t tell us exactly how much satisfaction is derived by the consumer from those combinations. This is because utility or satisfaction is a mental phenomenon and can not be measured in absolute terms. That is why, we level indifference curve as I, II, III, etc. showing that higher indifference curves provide a greater level of satisfaction but we can not say how much greater.

On the other hand, we can level iso-product curves in the physical units of the output produced. Moreover, if we have an iso-product map showing various iso-product curves, it is possible to say by how much production is greater or less on one iso-product curve than on another.

Isoquant Map

A number of isoquants representing the different amount of output are known as isoquant map. A higher isoquant curve shows a higher quantity of output.

Marginal Rate of Technical Substitution

The marginal rate of technical substitution of X for Y is the number of units of factor Y which can be replaced by one unit of factor X, quantity of the output remains unchanged.

Combinations	Factor-X	Factor-Y	MRTS of X for Y
A	1	12	---
B	2	8	4:1
C	3	5	3:1
D	4	3	2:1
E	5	2	1:1

In this table, various combinations of factors X and Y yield output equal to 100 units of the product. In combination B, four-unit of factor Y can be replaced by one unit of factor X without any change in output. Therefore 4:1 is the marginal rate of technical substitution (MRTS) at this stage.

Now, in combination C, only three units of factor Y can be replaced by one unit of factor X without any loss of output. Therefore, here the MRTS is 3:1. Similarly, between C & D, is 2:1 and D & E is 1:1.

Algebraically, it can be stated that:

It shows that as the quantity of factor X is increased relative to the quantity of Y, the number of units of Y that will be required to be replaced by one unit of factor X will diminish, the quantity of the output remains unchanged. This is known as the Law of Diminishing Marginal Rate of Technical Substitution.

As the quantity of factor X is increased, and the quantity of factor Y is decreased, the marginal productivity of factor X will diminish and the marginal productivity of factor Y will increase. Therefore, less and less of Y will be required to be replaced one unit of X to maintain the same level of output as more and more of X and less of Y is used

The slope of the isoquant is equal to the relative marginal productivities of the two variable factors.

Assumptions:

The main assumptions of Iso-quant curves are as follows:

1. Two Factors of Production:
There are only two inputs: labor and capital to produce a commodity.

2. Divisible:
Factors of production are divisible and can be divided into small parts.

3. Constant Technique:
The technology of production is given and it should remain constant.

4. Possibility of Technical Substitution:
The technical substitution between the two factors is possible. The two inputs: labor and capital can substitute each other but at a diminishing rate.

Properties / Characteristics of Isoquant Curve: 

1. An isoquant curve slopes downward from left to right: i.e., it has a negative slope. The negative slope of isoquant implies substitutability between inputs. it denotes that if one of the input [Capital] decreases, the other input [Labor] must increase so that the total output remains unaffected.

2. Every Isoquant to the right represents a higher level of output than that of Proceeding One: As the producer move to the right he reaches the higher isoquant curve and it represents a higher level of output than the lower one.

3. The Isoquant curve can not intersect or be tangent to each other: If they did, the point of their intersection would supply the same levels of output, which is not possible. This property follows from the fact that two isoquants represent different levels of output that need different combinations of two variable inputs.

4. Isoquants are convex to origin: Convexity of isoquants implies not only the substitution between the inputs but also diminishing marginal rate of technical substitution between the inputs in the economic reason.

MRTS decreases for two reasons:

• No factor is a perfect substitute for another.
• Inputs are subject to diminishing marginal return.

5. Isoquants show cardinal quantity : Isoquants indicate physical magnitudes that are cardinally measured such as 20 units, 40 units, 100 units, etc. The output can be identified on each isoquant by the numbers attached to isoquants.

Isoquant map, Ridge lines and Economic Region of Production:

An isoquant map is a set of  isoquants representing different combinations of inputs with different levels of output as shown by isoquants IP1, IP2, IP3, IP4 and IP5. Each successive upper isoquant indicates a higher level of output than the lower ones.

The whole isoquant map or production-plane is not technically efficient.The reason is that, on a convex isoquant, the MRTS decreases along the isoquant. The limit to which the MRTS can decrease is zero. A zero MRTS implies that there is a limit to which one input can substitute another. It also determines the minimum quantity of an input which must be used to produce a given output.

Such a point on an isoquant can be obtained by drawing a tangent to the isoquant and parallel to the horizontal and the vertical axis. By joining these points A,B,C,D,E, we get the upper ridge line, similarly, by joining the points F,G,H,I,J, we get the lower ridge line. The ridge lines are locus of points on the isoquants where the marginal products[MP] of the inputs are equal to zero. The upper ridge line implies that MP of capital is zero along the line, OE. The lower ridge line implies that MP of labour is zero along the line, OJ.

The area between the two ridge lines is called ’economic region’ or ‘technically efficient region’ of production. Any capital- labour combination or production technique, within the economic region is technically efficient to produce a given output. Any production technique outside this region is technically inefficient since it requires more of both inputs to produce the same quantity.

Other forms of Isoquants:

1. Linear Isoquants: A linear isoquants implies perfect substitutability between the two inputs Capital and Labour. If the two factors are perfect substitute for each other, then there is no problem attached to replacing capital with labour or vice versa. A linear isoquant also implies that the MRTS between both factors remains constant throughout.

2. L-Shaped Isoquants or Fixed Factor-Proportion: If two variable factors are perfect complement to each other, so that an increased use of one variable factor will require a corresponding increase in the units of the related factor. Such an isoquant implies zero substitutability between two factors. It also implies that if the quantity of one factor is increased without changing the quantity of other factor, there will be no change in output. The output can be increased only by increasing  the quantity of both the inputs proportionately.

It is clear from the above diagram that if the units of only labour or only capital are increased, output will not increase. The units of both inputs have to be increased proportionately if the producer wants to increase the production. This kind of technological relationship between both inputs gives a fixed proportion production function. It is also called Leontief function.

Kinked or Linear Programming Isoquants: Kinked  isoquants represents different combinations of two inputs. It assumes that there are only a few processes to produce any one commodity and substitutability of the factors is possible only at the kinks of the curve. This form is also called ‘Activity Analysis Isoquant’ or ‘linear-programming Isoquant’, as it is basically used in Linear-Programming.

In the above diagram, each of the points on the kinked isoquants represents a combination of two inputs- capital and Labour that can produce the given quantity of the output. On a kinked isoquants, only kinks are the technically feasible points.

Dr. Swati Gupta

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